Basic Math Examples

$8 a^{2} \cdot (2 a^{- 7}) \cdot (4 w^{- 7} y^{- 2} y^{3} w)$

Step 1

Multiply $a^{2}$ by $a^{- 7}$ by adding the exponents.

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Step 1.1

Move $a^{- 7}$ .

$8 (a^{- 7} a^{2}) \cdot 2 \cdot (4 w^{- 7} y^{- 2} y^{3} w)$

Step 1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$8 a^{- 7 + 2} \cdot 2 \cdot (4 w^{- 7} y^{- 2} y^{3} w)$

Step 1.3

Add $- 7$ and $2$ .

$8 a^{- 5} \cdot 2 \cdot (4 w^{- 7} y^{- 2} y^{3} w)$

Step 2

Multiply $w^{- 7}$ by $w$ by adding the exponents.

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Step 2.1

Move $w$ .

$8 a^{- 5} \cdot 2 \cdot (4 (w \cdot w^{- 7}) y^{- 2} y^{3})$

Step 2.2

Multiply $w$ by $w^{- 7}$ .

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Step 2.2.1

Raise $w$ to the power of $1$ .

$8 a^{- 5} \cdot 2 \cdot (4 (w^{1} w^{- 7}) y^{- 2} y^{3})$

Step 2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$8 a^{- 5} \cdot 2 \cdot (4 w^{1 - 7} y^{- 2} y^{3})$

Step 2.3

Subtract $7$ from $1$ .

$8 a^{- 5} \cdot 2 \cdot (4 w^{- 6} y^{- 2} y^{3})$

Step 3

Multiply $y^{- 2}$ by $y^{3}$ by adding the exponents.

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Step 3.1

Move $y^{3}$ .

$8 a^{- 5} \cdot 2 \cdot (4 w^{- 6} (y^{3} y^{- 2}))$

Step 3.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$8 a^{- 5} \cdot 2 \cdot (4 w^{- 6} y^{3 - 2})$

Step 3.3

Subtract $2$ from $3$ .

$8 a^{- 5} \cdot 2 \cdot (4 w^{- 6} y^{1})$

Step 4

Simplify $8 a^{- 5} \cdot 2 \cdot (4 w^{- 6} y^{1})$ .

$8 a^{- 5} \cdot 2 \cdot (4 w^{- 6} y)$

Step 5

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$8 \frac{1}{a^{5}} \cdot 2 \cdot (4 w^{- 6} y)$

Step 6

Combine $8$ and $\frac{1}{a^{5}}$ .

$\frac{8}{a^{5}} \cdot 2 \cdot (4 w^{- 6} y)$

Step 7

Multiply $\frac{8}{a^{5}} \cdot 2$ .

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Step 7.1

Combine $\frac{8}{a^{5}}$ and $2$ .

$\frac{8 \cdot 2}{a^{5}} \cdot (4 w^{- 6} y)$

Step 7.2

Multiply $8$ by $2$ .

$\frac{16}{a^{5}} \cdot (4 w^{- 6} y)$

Step 8

Rewrite using the commutative property of multiplication.

$4 \frac{16}{a^{5}} w^{- 6} y$

Step 9

Multiply $4 \frac{16}{a^{5}}$ .

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Step 9.1

Combine $4$ and $\frac{16}{a^{5}}$ .

$\frac{4 \cdot 16}{a^{5}} w^{- 6} y$

Step 9.2

Multiply $4$ by $16$ .

$\frac{64}{a^{5}} w^{- 6} y$

Step 10

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{64}{a^{5}} \cdot \frac{1}{w^{6}} y$

Step 11

Combine.

$\frac{64 \cdot 1}{a^{5} w^{6}} y$

Step 12

Multiply $64$ by $1$ .

$\frac{64}{a^{5} w^{6}} y$

Step 13

Combine $\frac{64}{a^{5} w^{6}}$ and $y$ .

$\frac{64 y}{a^{5} w^{6}}$